Tex. R. Civ. P. 159
As amended through February 20, 2024
In cases arising under the provisions of the title relating to injuries resulting in death, the suit shall not abate by the death of either party pending the suit, but in such case, if the plaintiff dies, where there is only one plaintiff, some one or more of the parties entitled to the money recovered may be substituted and the suit prosecuted to judgment in the name of such party or parties, for the benefit of the person entitled; if the defendant dies, his executor, administrator or heir may be made a party, and the suit prosecuted to judgment.
Tex. R. Civ. P. 159